Uric acid is a decomposition product of the metabolism of purines (in DNA and RNA). It is transported by the blood and excreted in the urine. Its solubility in water (maximum possible concentration in a saturated solution) is about $0.2\;\frac{g}{L}$.
The urine of a normal adult contains a total of $7\;\frac{g}{L}$ of uric acid and urate sodium (soluble).
The acidity constant of uric acid is $4.0\cdot10^{-6} \frac{mol}{L}$ .
Calculate the $pH$ range where uric acid precipitates into urine forming kidney stones.
Uric acid : weak acid
The precipitation happens when we have more than $0,2\;\frac{g}{L}$ $=$ $0.0012\;\frac{mol}{L}$ uric acid $HB$ and so less than $6,8\;\frac{g}{L}$ $= $ $0.0358\;\frac{mol}{L}$ sodium urate $B$
$\frac{[HB]}{[B]}$ $\gt$ $ \frac{0.0012}{0.0358}$
$\frac{[HB]}{[B]}$ $=$ $\frac{[H_3O^+]}{K_a}$
thus:
$[H_3O^+]$ $\gt$ $ \frac{0.0012}{0.0358}K_a$
$-log[H_3O^+]$ $\lt$ $-logK_a$ $-$ $log\frac{0.0012}{0.0358}$
$pH$ $\lt$ $ -log4,0 \;10^{-6}$ $-$ $log\frac{0.0012}{0.0358}$
$pH$ $\lt$ $ 5.40$ $+$ $1.47$
$pH$ $\lt$ $ 6.87$
